How many golf balls can fit in a Boeing 747?

[Ryan]

Let's kick this off with an oldie but goodie...that I shamelessly stole from the Practice section :)

It's been a while since I did fermi questions, plus I'm guessing everyone can do with a little warmup.

[Holden McGinnis]

I'd say 7.  My logic is mainly based on assuming the boeing is a cylinder with r = 3m and h = 70 m, this should include all cargo and passenger space more or less.  So then 3*3^2*70 = 1.5E3 m^3 or 1.5E9 cm^3.  I assume a golf ball has a radius of about 2 cm, thus has volume of 3.2E1 cm^3.  I assume that because of spherical packing density only maybe 75-80% of the volume is utilized thus we end up with ~1E9 usable cm^3 and 3.1E7 golf balls.

If the United States was covered in a layer of rain one inch thick, how many toilets could be flushed using that water?

[Ryan Menezes]

Wow, spot on. My exact computation says 31.1 million. My sources were

http://en.wikipedia.org/wiki/Close-packing_of_spheres

http://www.wolframalpha.com/input/?i=ping+pong+ball (about the same size as a golf ball)

http://www.boeing.com/commercial/747family/pf/pf_domestic_prod.html

As for the rain question, I'm a bit rusty so I'm going to make some mistakes but here goes! I did this on paper, here's the transcription:

Main assumptions:

• I think I recall US coastline is 12k miles, so let's pretend the US is circular so I can compute area :)
• Guess: a toilet flush takes 3 gallons.
• Guess: 3 gallons is about 12 * 9 * 9 inches^3 (approximate dimensions of a milk jug?)
• Approximation: one mile is 5E3 feet

Numerator is cubic miles of rain:

pi * (12 E 3 circumference in miles * (1 radius / 2 pi circumference))^2 * 1 inch / (12 * 5E3 miles)

...which is ~2E2 using pi=3

Denominator is cubic miles of water per toilet flush:

3 gal * (12 * 9 * 9 in^3 / gal) * (1 / (12 * 5E3))^3

...which is ~1.5E-11 using the intermediate approximations 12*9*9=1E3 and 6^3=2E2

The overall answer is ~1E13, so 13. At all close?

--
 
 

--
current project: http://www.fermiquestions.com

[Holden McGinnis]

Very good!  I had 4E13.  

Sources:

http://en.wikipedia.org/wiki/United_States

The toilet in my house that has 1.6 Gpf written on it, which I took to be fairly standard.

9.8E12 square meters is 1.5E16 square inches, with a height of 1 in is 1.5E16 cubic inches, which is more or less 1E13 cubic feet.  7 gallons in a cubic foot so 7E13 gallons and then divide by 1.6 and boom 4E13 flushes.  

[Ryan Menezes]

Cool, I'm glad I did ok on that.

The hardest part of fermi questions for me is taking the risk of being horribly wrong. But that's the only way to learn!

How many Facebook "likes" happen over the course of a year?

--
 
 

[Ryan Menezes]

How many Facebook "likes" happen over the course of a year?

(resending that last question now that more folks have joined this list)